Gaussian Based Non-linear Function Approximation for Reinforcement Learning

Abbas Haider, Glenn Hawe, Hui Wang, Bryan Scotney

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)
117 Downloads (Pure)


Reinforcement learning (RL) problems with continuous states and discrete actions (CSDA) can be found in classic examples such as Cart Pole and Puck World, as well as real world applications such as Market Making. Solutions to CSDA problems typically involve a function approximation (FA) of the mapping from states to actions and can be linear or nonlinear. Linear FAs such as tile-coding (Sutton and Barto in Reinforcement learning, 2nd ed, 2009) suffer from state information loss due to state discretization, whilst non-linear FAs such as DQN (Mnih et al. in Playing atari with deep reinforcement learning,, 2013) are practically infeasible in infinitely large state spaces due to their cubic time complexity (O(n3)). In this paper, we propose a novel, general solution to CSDA problems, called Gaussian distribution based non-linear function approximation (GBNLFA). Experimentation on three CSDA RL problems (Cart Pole, Puck World, Market Marking) demonstrates the superiority of GBNLFA over state-of-the-art FAs, namely tile-coding and DQN. In particular, GBNLFA resolves the state information loss problem with linear FAs and provides an asymptotically faster algorithm (O(n)) than linear FAs (O(n2)) and neural network based nonlinear FAs (O(n3)).
Original languageEnglish
Article number223
Pages (from-to)223
JournalSN Computer Science
Issue number3
Early online date20 Apr 2021
Publication statusPublished (in print/issue) - 20 Apr 2021


  • Function approximation
  • Reinforcement learning
  • Gaussian distribution
  • Probability density function


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